Question

There are ________ rational numbers between two rational numbers.
A. Infinite
B. Two
C. One
D. None of these

Answer 1

Hint: As we know if we multiply the same number in the numerator and denominator of a rational number then it’s value doesn’t change. By using this property we can insert as many as rational numbers between two rational numbers.

Complete step by step solution:
We can insert infinite rational numbers between two rational numbers.
For example if we have two rational numbers are $\dfrac{1}{10}$ and $\dfrac{9}{10}$.
So we can insert easily as $\dfrac{2}{10},\dfrac{3}{10},\dfrac{4}{10},\dfrac{5}{10},\dfrac{6}{10},\dfrac{7}{10},\dfrac{8}{10}$
Now if we change denominator as
$\dfrac{1}{10}=\dfrac{10}{100}$
$\dfrac{9}{10}=\dfrac{90}{100}$
Now we can insert rational number between $\dfrac{10}{100}$ and $\dfrac{90}{100}$ as $\dfrac{11}{100},\dfrac{12}{100},\dfrac{13}{100},\dfrac{14}{100},\dfrac{15}{100},\dfrac{16}{100},.....................\dfrac{89}{100}$
Now we can change denominators further and continue this process.
So we can easily say that we can insert infinite rational numbers between two numbers.

Option A is correct.

Note: Rational numbers are that number which we can write as $\dfrac{p}{q}$ form where p is numerator and q is denominator. In this denominator can never be equal to zero.